All lens design forms have limiting aberrations. The proposed classes of lenses can be corrected for all 3rd and 5th order ray aberrations. The limiting aberrations are seventh order or higher. A variety of these lenses are disclosed here for the sake of example. These lens design forms can be used in various applications including the objective lens for an endoscope or other optical instrument.
Aberrations
An optical aberration is a defect in the image forming capability of a lens or optical system, and may be considered to be a departure of the performance of an optical system from the predictions of paraxial optics. In an imaging system, it occurs when light from one point of an object does not converge into (or does not diverge from) a single point after transmission through the system.
Aberrations can be expressed as discrepancies from paraxial theory. In terms relating to the underlying mathematics of the system, aberrations can be categorized as first order, third order, fifth order, seventh order, etc.
First Order Aberrations
Chromatic aberration arises because the index of refraction of a material is different for light of different wavelengths. First order chromatic aberration consists of two components, focus shift, and magnification differences for various wavelengths. A common example of this effect is observed when white light striking a prism breaks up into colored rays. As result of this effect, the image formed by a lens will be different for each color component of light.
Third Order Aberrations
For finite field angles and apertures, light rays do not focus neatly at a point. Accordingly, no precise image is formed. These deviations from focus may be described by third order theory in terms of the five “Seidel” aberrations. These are monochromatic aberrations characterized by certain geometric effects.
Spherical aberration—Spherical aberration is an axial aberration and so may be completely described by meridional rays. Light rays in the paraxial region focus at a different point than light rays going through the periphery of the lens. The distance between the two foci is the lateral spherical aberration. The case where the peripheral rays are more bent than the paraxial rays is called positive spherical aberration. The case where the peripheral rays are bent and the peripheral focus is farther from the lens, is called negative spherical aberration. The lateral spherical aberration is proportional to the square of the entrance pupil diameter.
Spherical aberration can be controlled by balancing surfaces having positive spherical aberration with surfaces having negative spherical aberration, or by using a small aperture stop.
Coma—Like spherical aberration, coma is an aperture dependent aberration. However, unlike spherical aberration it only affects off-axial rays. The comatic blur is asymmetric and “comet shaped”, hence the name coma.
Coma may be eliminated in a lens by appropriate choice of curves. It may be minimized by using a small aperture stop
Curvature of field—In curvature of field a plane object is sharply imaged, but on a curved surface. The surface on which the image is formed is called the Petzval surface.
Curvature of field may be corrected by balancing components contributing negative field curvature with components contributing positive field curvature.
Distortion—In distortion, the object is sharply imaged but does not retain its shape. There are two kinds of distortion, barrel distortion and pincushion distortion, so named because of their effect on the image of a square grid target.
Distortion can be corrected by balancing surfaces contributing barrel distortion to those contributing pincushion distortion. A perfectly symmetric system will have no distortion. Changing the aperture size has no effect on distortion.
Astigmatism—Astigmatism refers to the differing focal positions for rays in the tangential and sagittal planes. While each plane focuses to a perfect point, in the astigmatic image these focus planes are not coincident. Astigmatism is not present on-axis, but increases as the field angle increases.
Astigmatism can be corrected by balancing components contributing negative astigmatism with components contributing positive astigmatism.
Fifth Order Aberrations
There are nine secondary or fifth-order aberrations:
Secondary spherical aberration—there is one form of fifth order spherical aberration, and there are two forms of fifth order oblique spherical aberration.
Secondary coma—there is one form of fifth order linear coma, and there are two forms of fifth order elliptical coma.
Secondary curvature of field—there is one form of fifth order sagittal field curvature.
Secondary distortion—There is one form of fifth order distortion.
Secondary astigmatism—there is one form of fifth order astigmatism
Optical Systems
A lens or group of lenses can be arranged to form an optical system. The lenses in such systems are typically arranged such that they are all coaxial with the same optical axis, although for some applications this may not necessarily be the case. Over the history of lens design, various categories of optical systems have been explored. Some examples of lens designs include five element lens designs, reverse telephoto lens designs, and Biogon™ type lens designs.
However, prior lens designs of each of these types have not been known to be correctable for all 3rd and 5th order aberrations.
It is therefore desired to provide lens design forms that account for these deficiencies